By Agustín Rayo
Este libro reune ensayos de los más grandes especialistas en el tema de los angeles 'cuantificación common' abordado desde todas sus dimensiones. Ellos no sólo se limitan a hablar sobre el tema sino que después del análisis que realizan, presentan avesadas tesis de cara a los problemas que se sucitan.
Lo recomiendo, pues, creo que si todavía no lo es, en el futuro se convertirá en un clásico.
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Extra info for Absolute Generality
But for us, it is the other way round; the quantifier ∀+ is to be understood in terms of the quantifier ∀. It is through a prior understanding of the quantifier ∀ that we come to appreciate that there is a sense of the quantifier ∀+ in which it is correct to suppose that some one thing has the objects in the range of ∀ as members. Thus far from presupposing that the all-in-one principle is true, we presuppose that it is false! Of course, there is some mystery as to how we arrive at this new understanding of the quantifier.
E. no interpretation of the quantifier is absolutely unrestricted, which would appear to be the desired general conclusion. But unfortunately, things are not so straightforward. For in something like the manner in which our opponent’s first-order quantifier over objects was shown not to be absolutely unrestricted, it may also be shown that our own second-order quantifier over interpretations is not absolutely unrestricted; and so (5G) cannot be the conclusion we are after. ⁴ Now associated with any ‘second-order’ interpretation M is a first-order interpretation I, what we may call the ‘sum’ interpretation, where our understanding of ∃I xϕ(x) is given by ∃M J∃J xϕ(x).
And given that one understands what it is for an arbitrary one of them to be true, how can one be willing to commit oneself to the truth of each of them without also being willing to commit oneself to the claim that each of them is true? But once one has committed oneself to this general claim, then the same old difficulties reappear. For we can use the quantifier ‘every instance’ ( just as we used the quantifier ‘every interpretation’) to construct an instance that does not fall within its range.
Absolute Generality by Agustín Rayo